Create an Equivalent Division Problem with a Whole Number Divisor
Create an Equivalent Division Problem with a Whole Number Divisor is a Grade 5 math skill from Eureka Math that teaches students to rewrite a decimal division problem so the divisor becomes a whole number. By multiplying both dividend and divisor by the same power of 10, students create an equivalent problem that is easier to solve. This technique uses the fundamental property of division and connects to fraction equivalence.
Key Concepts
A division expression can be rewritten as a fraction and then multiplied by a form of 1 (such as $\frac{10}{10}$ or $\frac{100}{100}$) to create an equivalent division problem with a whole number divisor. $$a \div b = \frac{a}{b} = \frac{a \times n}{b \times n}$$.
Common Questions
How do you create an equivalent division problem with a whole number divisor?
Multiply both the dividend and the divisor by the same power of 10 to eliminate the decimal in the divisor. For example, 4.8 ÷ 0.6 becomes 48 ÷ 6 by multiplying both by 10.
Why does multiplying dividend and divisor by the same number give an equivalent problem?
Because division is equivalent to a fraction, and multiplying numerator and denominator by the same number does not change the fraction value. So 4.8/0.6 = 48/6.
What is the property of division that allows this transformation?
The property states that a ÷ b = (a x n) ÷ (b x n) for any nonzero n. This is equivalent to finding an equal fraction by multiplying numerator and denominator by the same value.
What Eureka Math Grade 5 chapter covers equivalent division with whole number divisors?
Eureka Math Grade 5 covers creating equivalent division problems in its decimal division chapters, preparing students for the standard long division algorithm with decimals.
How does this skill help with decimal long division?
Converting to a whole number divisor lets students use familiar whole number long division procedures instead of learning a new algorithm for decimal divisors.